Knowing When to Stop Matters: A Unified Algorithm for Online Conversion under Horizon Uncertainty

TL;DR

This paper introduces a unified online conversion algorithm that optimally handles horizon uncertainty and practical constraints, with a learning-augmented version that adapts to horizon predictions for improved performance.

Contribution

It presents a novel algorithm achieving optimal guarantees across different horizon models and extends it with a learning-augmented approach for adaptive performance based on horizon predictions.

Findings

Achieves optimal competitive guarantees under various horizon models.

Extends to a learning-augmented version leveraging horizon predictions.

Maintains strong performance even with unreliable horizon predictions.

Abstract

This paper investigates the online conversion problem, which involves sequentially trading a divisible resource (e.g., energy) under dynamically changing prices to maximize profit. A key challenge in online conversion is managing decisions under horizon uncertainty, where the duration of trading is either known, revealed partway, or entirely unknown. We propose a unified algorithm that achieves optimal competitive guarantees across these horizon models, accounting for practical constraints such as box constraints, which limit the maximum allowable trade per step. Additionally, we extend the algorithm to a learning-augmented version, leveraging horizon predictions to adaptively balance performance: achieving near-optimal results when predictions are accurate while maintaining strong guarantees when predictions are unreliable. These results advance the understanding of online conversion under various degrees of horizon uncertainty and provide more practical strategies to address real world constraints.